Our study aims for a better understanding of the statistical properties
of GANs and can be seen as complementary to the existing vast literatures
on computational GAN training algorithms and practical GAN applications.
In this paper we have considered only the original [1]}
formulation of the GAN problem. Extensions to the numerous other existing
GAN variants, such as the popular Wasserstein GAN of [2]},
would be of interest and would bring the statistical theory closer to the
machine learning practice. Related minimax problems in non-GAN settings
in machine learning and elsewhere could also be considered.
Finally, the focus in this paper has been purely theoretical
and exploring the use of our results in practical GAN applications
would be interesting.
